Cremona's table of elliptic curves

1694 = 2 · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2+ 7- 11-	Signs for the Atkin-Lehner involutions
Class	1694d	Isogeny class
Conductor	1694	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	21265990680661496 = 23 · 7 · 1114	Discriminant
Eigenvalues	2+  0  2 7- 11- -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-73046,-2899748]	[a1,a2,a3,a4,a6]
Generators	[-1257:17671:27]	Generators of the group modulo torsion
j	24331017010833/12004097336	j-invariant
L	2.3730703470768	L(r)(E,1)/r!
Ω	0.30543476545973	Real period
R	7.7694834230967	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13552m4 54208bd3 15246bv4 42350bt3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1694d3

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	0	2	-	-	-2	-2	0	-8	2	-8	-2	-10	-4	8	6	0	-10	-12	16	14	0	0	-6	10

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Quadratic twists for elliptic curve 1694d3

-4	8	-3	5	-7	-11
13552m4	54208bd3	15246bv4	42350bt3	11858i4	154b4

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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